Problem: Simplify the following expression: $t = \dfrac{-55n^3 - 110n^2}{11n^2}$ You can assume $n \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-55n^3 - 110n^2 = - (5\cdot11 \cdot n \cdot n \cdot n) - (2\cdot5\cdot11 \cdot n \cdot n)$ The denominator can be factored: $11n^2 = (11 \cdot n \cdot n)$ The greatest common factor of all the terms is $11n^2$ Factoring out $11n^2$ gives us: $t = \dfrac{(11n^2)(-5n - 10)}{(11n^2)(1)}$ Dividing both the numerator and denominator by $11n^2$ gives: $t = \dfrac{-5n - 10}{1}$ or more simply, $t = -5n - 10$